| On Global Dimensions of $A_n$-Type Finite Dimensional Algebras |
| Received:August 23, 2014 Revised:March 04, 2015 |
| Key Words:
global dimension finite dimensional $k$-algebra quiver admissible ideal
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11371307). |
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| Abstract: |
| A technique is provided to explicitly describe global dimensions of all $A_{n}$-type finite dimensional $k$-algebras for $k$ an algebraic closed field. All possible global dimensions of all $A_n$-type finite dimensional algebras are explicitly presented. In particular, it is pointed out that the maximum is $n-1$, and the minimum is $1$ for $n>1$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.04.003 |
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